Can’t correct category count for default

My category counts have been way high (like saying 800 when there are really only 80) for a long time (years) now. Clearing the cache has no effect. But I figured out a laborious way to manually fix them through a process of renaming, deleting and recreating category names and reassigning posts (a pain, but I found a way to make it manageable). It works for every category except the default category.

In the default category I can’t remove non-existent links by renaming, reassigning and then reassigning things back like the other categories. Not only that, but it seems to add a new ghost post to the default category count for every ghost I eliminate from the other categories!

This is a largish old site that has been moved a number of times, so I suspect there is a database problem or some other long gone link still tied to it.

Does anyone have suggestions of how to troubleshoot/solve this? It doesn’t seem to be a plugin issue.

The page I need help with: [log in to see the link]